# Mathematics and Computational Thinking

- MCT 121: Mathematics 7
- MCT 221 Mathematics 8
- MCT 201: Algebra I
- MCT 301: Geometry
- MCT 321: Integrated Mathematics
- MCT 421: Algebra II
- MCT 422: Accelerated Algebra II
- MCT 501: Functions, Statistics and Trigonometry (FST)
- MCT 511: Introductory Statistics
- MCT 521: Pre-Calculus
- MCT 552: Introduction to Python Programming
- MCT 611: Accelerated Pre-Calculus
- MCT 621: Calculus
- MCT 651: Advanced Computer Science Principles
- MCT 711: Advanced Statistics
- MCT 721: Advanced Calculus I
- MCT 722: Advanced Calculus II
- MCT 752: Advanced Computer Science
- MCT 821: Multivariable Calculus
- MCT 822: Linear Algebra
- MCT 851: Topics in Programming

## MCT 121: Mathematics 7

Focusing on algebra and geometry, this course is designed to create the transition from basic number operations to more complex mathematical problems. The course begins with topics that involve whole numbers, fractions, real numbers, and arithmetic, and connects these concepts with simple algebraic expressions and real-life word problems. Students are then introduced to rates, ratios and percentages, applying the algebra they learnt earlier to more complex word problems. In the geometry portion of the course, the students explore angles, triangles and polygons as well as the area, volume and surface area of simple geometric shapes.

*Prerequisites: Department consent *

## MCT 221 Mathematics 8

This course is designed to lay the foundations of first year algebra and geometry. The algebra topics of study include equations, proportions and inequalities in one variable, writing, solving and graphing linear equations and systems of linear equations, operations involving polynomials, fractions and exponents, factoring and solving quadratic equations, and data analysis. In the geometry portion of the course, constructions, investigations, proofs and projects are used to explore the various facets of geometry. Upon completion of the course, students should have a firm grasp of Euclidean geometry.

*Prerequisites: Completion of Math 7 and department consent *

## MCT 201: Algebra I

This is a course in first-year algebra with a focus on numerical, algebraic, graphing and verbal methods of problem-solving. The algebra topics of study include equations, proportions, and inequalities in one variable, writing, solving and graphing linear equations and inequalities, solving and graphing systems of linear equations, operations involving polynomials and factoring, solving quadratic equations, fractions, exponents and data analysis. Following Algebra I, students take either Integrated Mathematics or Geometry.

*Prerequisites: Department consent *

## MCT 301: Geometry

This course is designed to provide a solid foundation of fundamental geometric concepts. By the end of the course, students have a firm and confident grasp of Euclidean geometry and are prepared for further studies in mathematics, namely Algebra II and beyond. Students enrolled in this class are immersed in topics relating to inductive and conductive reasoning, spatial reasoning, triangle congruence and similarity, properties of different polygons and their application on coordinate planes, perimeters, areas, volumes, ratios and proportions, as well as trigonometric ratios and properties.

*Prerequisites: Department consent*

## MCT 321: Integrated Mathematics

Covering foundational topics in algebra, geometry and data analysis, Integrated Mathematics is the stepping stone for all higher-level math courses. It enables students from a range of mathematical backgrounds to tackle challenging problems with a variety of approaches and to improve their critical thinking skills. The algebra topics of study include writing, solving and graphing linear equations and inequalities, solving and graphing systems of linear equations, operations involving polynomials and factoring, solving quadratic equations, percentages, and exponents and radicals. The geometry topics of study include the properties of lines in a plane, right triangles including trigonometric ratios, circles, area and volume. In data analysis, students study cover measurements of central tendency, representations of data, and general analysis.

*Prerequisites: Department consent*

## MCT 421: Algebra II

The understanding of functions and their behavior is fundamental to the study of advanced Algebra. In this course, students explore different functions and their properties including linear functions, quadratic functions, polynomial functions, absolute-value functions, exponential functions, logarithmic functions, rational functions, radical functions and piecewise functions. Students also learn how to use their graphing calculators as a tool of understanding functions’ behaviors. The course also introduces other topics such as imaginary numbers, matrices, probability and statistics, and right triangle trigonometry. This course serves as an introduction to managing advanced mathematical concepts. A graphing calculator is required.

*Prerequisites: Completion of Algebra I and Geometry or Integrated Mathematics*

## MCT 422: Accelerated Algebra II

Accelerated Algebra includes conic sections, series and sequences and partial fractions along with all Algebra II topics (linear functions and systems, absolute-value functions, matrices, quadratic and polynomial functions, exponential and logarithmic functions, radical and rational functions, piecewise functions, right triangle trigonometry and probability and statistics) with particular emphasis on challenging word problems and applications of the concepts. This course is an excellent choice for students who want to further develop their critical thinking and problem-solving skills and prepare well for the Accelerated Pre-Calculus course the year after. A graphing calculator is required.

*Prerequisites: Completion of Geometry or Integrated Mathematics and department consent*

## MCT 501: Functions, Statistics and Trigonometry (FST)

This course is designed to integrate functions, statistics and trigonometry and apply the algebra and geometry that students have studied in prior years. Supplementing the material presented in Algebra II in particular, FST completes the study of the elementary functions; linear, quadratic, exponential, logarithmic and trigonometric. Additionally, the course develops some material from finite mathematics including an introduction to probability and statistics, and additional applications of trigonometry, as well as sequences and series. This course contains many topics of traditional Pre-Calculus courses. These cover a wide range of mathematics and are designed to significantly enhance students' ability to undertake the study of advanced statistical applications. Throughout the course, modeling of real phenomena is emphasized. In this way, Functions, Statistics and Trigonometry demonstrates how a single mathematics course can involve all of the major areas of mathematics. A graphing calculator is required.

*Prerequisites: Algebra II and department consent *

## MCT 511: Introductory Statistics

From opinion polls and customer satisfaction surveys to drug trials, people seem to be surrounded by data everywhere. The importance of statistical literacy has been steadily increasing over the years, and data analyses often drive decision-making. Thus, students taking this course will rarely question the relevance of course content to real life. Introductory Statistics is primarily a project-based course in which students often collect and analyze their own data. They study proper collection and inference techniques to determine the significance of the data they collected. Students also learn how to build probability models by observing data and design experiments to reduce variability. A graphing calculator is required.

*Prerequisites: Functions, Statistics and Trigonometry or Pre-Calculus and department consent*

## MCT 521: Pre-Calculus

Pre-Calculus is not a specific, discrete study in mathematics, but rather a course that focuses upon establishing the student's knowledge and skills in preparation for undertaking more advanced math studies. While many of the topics introduced in Algebra II are revisited, they are covered in greater depth and breadth. The course includes more challenging studies in functions, conic sections, advanced trigonometry, and arithmetic and geometric series. The course explores functions and the analysis of their domains and ranges, recognition of families of curves, and their transformations. Topics in Trigonometry include triangle trigonometry, trigonometric functions, and analytic trigonometry, as well as applications of trigonometry including vectors, parametric equations and polar coordinates. A graphing calculator is required.

*Prerequisites: Algebra II, Accelerated Algebra II or FST, and department consent*

## MCT 552: Introduction to Python Programming

This introductory-level course is for students new to programming and computer science. It emphasizes computational thinking and helps develop the ability to solve complex problems. The course covers the basic building blocks of programming along with other central elements of computer science. It gives a foundation in the tools used in computer science and prepares students for further study in computer science, including Advanced Computer Science Principles and Advanced Computer Science courses.

*Course length: One semester*

## MCT 611: Accelerated Pre-Calculus

Accelerated Pre-Calculus consolidates algebra and geometry skills and focuses on the application and synthesis of those topics in preparation for Advanced Calculus. In addition to most Pre-Calculus topics (with an emphasis on trigonometric functions, applications and identities), the course covers calculus topics and applications in limits, differentiation and integration. Problems are solved numerically, graphically and algebraically, and a graphing calculator is used extensively for modeling and analyzing functions.

*Prerequisites: Accelerated Algebra II and department consent*

## MCT 621: Calculus

This course covers all of the first semester as well as some of the second semester topics of a college-level calculus survey course. Included are studies in limits and continuity, derivatives and integrals and selected applications of them and an introduction to differential equations. Pre-Calculus topics are reviewed when appropriate to ensure contextual presentation of new material. A graphing calculator is required.

*Prerequisites: Pre-Calculus and department consent *

## MCT 651: Advanced Computer Science Principles

Advanced Computer Science Principles introduces students to the central ideas of computer science, instilling the ideas and practices of computational thinking and inviting students to understand how computing changes the world. The rigorous course promotes deep learning of computational content, develops computational thinking skills, and engages students in the creative aspects of the field. The course is unique in its focus on fostering creativity in students. Students are encouraged to apply creative processes when developing computational artifacts and to think creatively while using simulations to explore questions that interest them. Rather than teaching a particular programming language or tool, the course focuses on using technology and programming as a means to solve computational problems and create exciting and personally relevant artifacts. Students design and implement innovative solutions using an iterative process similar to what artists, writers, computer scientists and engineers use to bring ideas to life. This course prepares students for the AP Computer Science Principles exam as well as the assessment that asks students to explore the implications of computing innovations and create a computer application.

*Prerequisites: Department consent. No prior computer science knowledge or experience is necessary*

## MCT 711: Advanced Statistics

This course follows the College Board Advanced Placement syllabus and is designed to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad-conceptual themes: exploring data (describing patterns and departures from patterns), sampling and experimentation (planning and conducting a study), anticipating patterns (exploring random phenomena using probability and simulation) and statistical inference (estimating population parameters and testing hypotheses). A graphing calculator is required. After the completion of this course, students are expected to take the AP Statistics Exam.

*Prerequisites: Pre-Calculus, Accelerated Pre-Calculus, or Functions, Statistics and Trigonometry and department consent *

## MCT 721: Advanced Calculus I

A rigorous and challenging course comparable to courses in colleges and universities, Advanced Calculus I is designed for students with excellent mathematical skills who seek college credit, college placement or both from institutions of higher learning. Based on the College Board Advanced Placement AB syllabus, the course approaches the calculus concepts (limits and continuity, derivatives and integrals and their applications) from multiple perspectives — graphically, analytically, numerically and verbally. A graphing calculator is required. After the completion of this course, students are expected to take the AP Calculus AB Exam.

*Prerequisites: Pre-Calculus or Accelerated Pre-Calculus and department consent*

## MCT 722: Advanced Calculus II

Designed as an extension of Advanced Calculus I rather than an enhancement, Advanced Calculus II includes, along with all Advanced Calculus I topics, additional topics such as: integration by parts and by tables, improper integrals, Euler’s Method and L’Hôpital’s Rule, infinite series, parametric equations, and polar coordinates and polar graphs. A graphing calculator is required. After the completion of this course, students are expected to take the AP Calculus BC Exam.

*Prerequisites: Accelerated Pre-Calculus or Advanced Calculus I and department consent*

## MCT 752: Advanced Computer Science

This course is based on the College Board AP Computer Science A syllabus which is equivalent to the first semester of a college level computer science course. The course develops the skills to write programs or part of programs to correctly solve specific problems. It also emphasizes the design issues that make programs understandable, adaptable and when appropriate, reusable. At the same time, the development of useful computer programs and classes is used as a context for introducing other important concepts in computer science, including the development and analysis of algorithms, the development and use of fundamental data structures and the study of standard algorithms and typical applications. In addition, an understanding of the basic hardware and software components of computer systems and the responsible use of these systems are integral parts of the course. The course uses Java as a tool to teach the methodology of object-oriented programming and problem-solving techniques through the development and usage of algorithms.

*Prerequisites: Introduction to Programming or its equivalent and department consent*

## MCT 821: Multivariable Calculus

Unlike Advanced Calculus I and II in which students study calculus of a single variable, Multivariable Calculus, a rigorous college course, focuses on functions of two or more independent variables. The concepts studied in this course are applied in many different fields — thermodynamics, electricity and magnetism, economics, modeling fluid or heat flow, etc. The topics included are vectors and the geometry of space, vector-valued functions, functions of several variables, multiple integration, vector analysis, and second order differential equations. A graphing calculator is required.

*Prerequisites: Advanced Calculus II*

## MCT 822: Linear Algebra

Widely used in both abstract algebra and functional analysis, linear algebra is the branch of mathematics concerned with the study of matrices, vectors and vector spaces, systems of linear equations and linear transformations. Linear algebra has extensive applications in engineering and technology, biology and life sciences, business and economics, physical sciences, and statistics and probability.

*Prerequisites: Advanced Calculus II*

## MCT 851: Topics in Programming

This class is for students who have completed Advanced Computer Science. Since there is no need to practice for the written AP exam, the class focuses solely on producing complex projects. Many students enrolled in Advanced Computer Science plan to pursue computer science in college – this course allows them to stay fresh and become more advanced coders, which will be a huge advantage at college. By the course’s end, students will have created several large, complex programs which they can show off as their own.** **

*Prerequisites: Advanced Computer Science*